A number of different effects of the violation of the equivalence principle (VEP), taken as subleading mechanism of neutrino flavor oscillation, are examined within the framework of the DUNE experiment. We study the possibility of obtaining a misleading neutrino oscillation parameter region caused by our unawareness of VEP. Additionally, we evaluate the impact on the measurement of CP violation and the distinction of neutrino mass hierarchy at DUNE. Besides, limits on VEP for a wide variety of textures of the matrix that connects neutrino gravity eigenstates to flavor eigenstates are imposed. An extra task of our study is to set limits on Hamiltonian added terms considering different energy dependencies (Ed-3, with d=3, 4, 5, 6) that can be associated to the usual Lorentz violating terms defined in the Standard Model extension Hamiltonian. In order to understand our results, approximated analytical three neutrino oscillation probability formulae are derived.